In the field of logging (e.g., wireline logging, logging while drilling (LWD), nuclear magnetic resonance (NMR) tools have been used to explore the subsurface based on the magnetic interactions with subsurface material. Some downhole NMR tools include a magnet assembly that produces a static magnetic field, and a coil assembly that generates radio frequency (RF) control signals and detects magnetic resonance phenomena in the subsurface material. Properties of the subsurface material can be estimated from the detected phenomena.
Downhole nuclear magnetic resonance can be used to provide information on pore size distributions, fluid saturations, fluid typing and permeability estimates. However, the measurements usually need to be calibrated. This is currently done in the lab environment using a well core. Well cores are very small compared to an entire formation, so multiple well cores are typically taken and analyzed and rock properties are interpolated in between geographic locations of the cores. Nevertheless, cores can be approximately a meter in length and 1/10 meter in diameter. Unfortunately, core analysis is expensive and time consuming. If the well is cored, the measurements required to calibrate the system can take weeks to months. Laboratory preparation (e.g., cleaning) and analysis of cores typically must be done off-site. Cores must be extracted and shipped to a laboratory for analysis and this can require significant time to complete. Further, physical lab experiments are difficult to perform due to the usual size and shape requirements of well samples such as cores, and the need to use sufficiently large sized samples to obtain accurate results by laboratory analysis.
Downhole NMR can be used to provide information on lithology independent porosity, pore size distributions, fluid properties, estimates of free and bound fluid and permeability. NMR functions by putting a sample in the presence of a strong magnetic field. The magnetic moments of the nuclei tend to align along the direction of the applied magnetic field (B0). The nuclei then precess around at a characteristic rate defined by:ω=−γB0 where ω is referred to as the Larmor frequency and γ is the gyromagnetic ratio, a fundamental constant specific to each NMR active isotope. The typical magnetic field strengths used in logging range from 0.01 T to 0.05 T such that ω is in the range of 400 kHz to 2 MHz, though other frequencies may be used.
In order to make an NMR measurement, the system must be excited away from the equilibrium. This is done by using an antenna to apply a radio frequency (rf) pulse at the Larmor frequency to tip the magnetic moments away from B0. As the nuclei's magnetic moments precess around the applied magnetic field, they induced a voltage in an antenna (either the same one that excited the system or a different one specifically for detection) that is measured as the NMR signal. By different combinations of rf pulses and delays, the measurement can be made sensitive to a range of different properties such as T1 relaxation, T2 relaxation or diffusion.
T1 relaxation is the time it takes for the magnetic moments of the nuclei to come back to equilibrium with the environment, i.e., return to alignment along the applied magnetic field. T2 is the time it takes the magnetic moments of the nuclei to come to equilibrium among themselves. When the system is initially excited, all the nuclei are precessing in unison. As time progresses, the nuclei interact with each other and their environment, such that they lose synchronicity. Eventually, at long enough time, all order between the precessing magnetic moments is lost and they will be in a completely disordered state. A diffusion measurement is used to measure the diffusion coefficients of the constituents present in the sample and can be used to determine fluids present. The diffusion coefficients of the fluids may be influenced by the sample pore structure.
While NMR can measure upon nearly every element of the Periodic Table, NMR in the oil industry focusses upon the 1H isotope. This is because the 1H isotope is abundant, common in the materials of interest, and has a high NMR sensitivity. Some work has been done to look at 13C and 23Na, but this has been limited to research due to the lower isotopic abundances and weaker signals from these isotopes.
Under ideal conditions, the NMR signal is proportional to the amount of hydrogen present in the system. For conventional reservoirs that consist of sandstones and carbonates, the rock matrix itself contains very little hydrogen. Therefore, the signal is assumed to arise from the fluids saturating the pore space. By inputting the hydrogen index of the fluids, the porosity of the system can be determined. Because information on the matrix is not required, NMR is referred to as lithology independent. This makes it valuable as other types of logging tools need to know the formation lithology in order to calibrate the porosity; using limestone for porosity calculation will produce incorrect values if the lithology is really dolomite. Because lithology may change numerous times throughout the borehole, this makes accurate assessment of porosity a challenge. For shale reservoirs, the matrix may contain significant quantities of clay and organic matter, which contains hydrogen, such that determining porosity from the NMR signal may not be as straight forward. Also, for both conventional and unconventional samples, if the sample is high in paramagnetic impurities, this may lead to loss of the NMR signal and therefore the calculated porosity will be too low.
Beyond porosity measurement, NMR can provide other valuable information about the system.
One of the other common uses of NMR is to obtain a pore size distribution (PSD). Fluids have a bulk NMR relaxation rate caused by internal interactions. For brine, this is usually on the order of 2-3 s. Paramagnetic impurities in the brine may lower this time. The bulk relaxation rate of oil depends on its viscosity. The relaxation rate of methane depends on pressure. When these fluid are placed in a porous medium, they will interact with the pore surfaces. When fluid molecules encounter pore surfaces, this will cause an enhancement in the relaxation rate from the bulk rate. The enhancement is governed by the surface relaxivity parameter. The larger the surface relaxivity, the more effective the surface is in enhancing the fluid relaxation. For T1, the equation relating pore size to measured T1 is simple:
            1              T        1              =                  ρ        1            ⁢              S        V              ,ρ1 is the surface relaxivity for T1, and S/V is the surface to volume ratio of the pore. S/V is used as a proxy for pore size; the smaller the pore, the larger its surface to volume ratio will be. As such, fluid molecules will encounter pore surfaces more frequently in small pores than in larger pores, causing the relaxation in the smaller pores to be more rapid than the larger pores. In order for the T1 to be considered a reflection of the pore size distribution, ρ1 must be constant throughout the pore space. The sample also needs to be in the fast diffusion regime, where fluid molecules rapidly explore the pore space but exchange between pores is slow, such that a single exponential decay value is produced for a pore of a given side. If the system is in the slow diffusion regime, the diffusion in the pore is slow compared to the relaxation. This occurs when either the surface relaxivity is very high or the pores are very large and will lead to bi- or multi-exponential decays from a single pore. If the exchange between pores is rapid, the system is said to be in the diffusional coupling regime. Here, the relaxation rates of the different pores will be averaged. This may be complete averaging, such that a single relaxation time is observed, or incomplete, where two peaks are still observed but with incorrect relaxation times and peak intensities.
The relaxation behavior for T2 relaxation is more complicated than T1. The observed T2 relaxation time is described by:
      1          T      2        =                    ρ        2            ⁢              S        V              +                            D          ⁢                                          ⁢                      γ            2                    ⁢                      G            2                    ⁢          Te                12            .      where ρ2 is the surface relaxivity for T2, SN is the surface to volume ratio of the pore, D is molecular diffusion constant, γ is proton gyromagnetic ratio, G is magnetic field gradient, and Te is interecho time.
In addition to the relaxation caused by differing pore sizes, the effective T2 relaxation rate can be influenced by the presence of magnetic gradients in the pore space. The magnetic gradients can arise naturally in the sample. These are referred to as internal gradients and they occur because of different magnetic susceptibility between the matrix and the saturating fluids. Because there cannot be a discontinuity in the magnetic field strength at the pore surface, magnetic gradients develop at the pore surfaces. The exact strength of the internal gradients depends on the pore shape, but the strength of the gradients can roughly be considered to be proportional to:
  G  ∝            Δχ      ⁢                          ⁢              B        0              r  where G is the strength of the internal gradient, Δχ is the difference in magnetic susceptibility between the pore matrix and saturating fluid and r is the pore radius. Magnetic gradients can also be applied, either through pulsed field gradients or through gradients that arise due to the design of the magnet. In order to minimise the effect of the second term, short echo spacings are used such that the effect T2 time can be approximated by:
      1          T      2        =            ρ      2        ⁢          S      V      and T2 can be thought to reflect the pore size distribution of the sample.
Both the T1 and T2 measurements give relative pore size distributions. In order for an absolute pore size distribution to be produced, the surface relaxivity needs to be determined. This is commonly done by calibration to MICP curves. However, this technique has the problem where MICP measures the pore throat size while NMR measures the pore body size. In some samples this is not an issue, but in other samples, there is frequently not a relationship. In shale samples, MICP measurements may damage the pore structure during measurement, such that the results are not an accurate reflection of the pore throat distribution. Other methods for determination of surface relaxivity relate to calibrating the relaxation times to pore size distributions measured from an imaging technique like X-ray CT or SEM. Alternatively, the surface relaxivity can be calibrated against the surface area measurements made through BET or N2 adsorption. Lastly, there are common values of surface relaxivity for different rock types that can be applied if calibration is not possible.
NMR can be used to help distinguish moveable from non-moveable fluids. This can be important for low-resistivity reservoirs. In these situations, there may be significant quantities of water present in the formation, but if the water is in very small pores, capillary pressure makes it immobile and hydrocarbons can be produced from the reservoir without a large watercut. Different lithologies have different rules of thumb for T2 cutoff times. Sandstones, the standard cutoff time is assumed to be 33 milliseconds (ms) while carbonates the cutoff time is 95 ms. Any signal below 3 ms is assumed to be associated with clay bound water. However, these are just rules of thumb and may vary significantly from formation to formation. Calibration is needed in order to determine the real T2 cutoff time or times for the reservoir.
NMR is also used to estimate permeability. While NMR is a static measurement and therefore does not actually measure permeability, a dynamic measurement, several of the parameters it measures can be related to permeability. There are several models used to convert the NMR data to permeability. One way of estimating permeability is the SDR or Kenyon method:k=C×T2LMa×Φb where k is permeability, C is a constant that typically 0.001, T2LM is NMR transverse decay time, ϕ is porosity, a=2 and b=4. This equation relates the pore size and porosity to permeability. The idea is that large pores and high porosity is likely to have a high permeability while samples with small pores and low porosity are likely to have lower permeability. Another method is the Timur-Coates. This relates the free and bound fluid ratios to permeability,
  k  =      C    ×          [                                    (                          FFI              BVI                        )                    a                ⁢                              (                          Φ              10                        )                    b                    ]      where k is permeability, C is typically 0.001, a=2 and b=4, ϕ is porosity, BVI is bulk volume irreducible fluid fraction, and FFI is free fluid fraction.
A third, less commonly used method is modifications of the Kozeny-Carman relation to relate to NMR measured properties. A frequently used equation is:
  k  =      Φ                  τ        ⁡                  (                      S            /            V                    )                    2      where k is permeability (e.g., in milliclarcies), ϕ is porosity, S/V is the surface to volume ratio of the pore, and τ is the tortuosity of the system. The tortuosity may be estimated from a variety of methods, but it often comes from diffusion measurements to relate the restricted diffusion rate to the unrestricted diffusion rate. In addition, there are other, less widely adopted methods to relate the NMR results to permeability that exist.
There may be minor differences in how these equations for calculating permeability from NMR results are written depending on the author and what the standard value of C is assumed to be. These equations can be applied uncalibrated, but the results are frequently shifted away from the true values by orders of magnitude. Because of surface relaxivity and structural differences in the rock matrix, the C term and frequently the A and B terms for a specific reservoir may differ from the standard values. The free and bound fluid estimates are frequently calculated with values estimated from using standard cutoff times, which may not be the true cutoff time for the reservoir. Both these effects make lab calibration of the equations important.
Beyond one dimensional measurements, two dimensional correlation measurements may be performed. The most common of these are the T2-Diffusion and the T1-T2 correlation measurements. The T2-diffusion is commonly used to perform fluid saturations. In the ideal situation, the diffusion axis will give information on the types of fluids present and the T2 axis will tell where the fluids are located in the pore space. However, interpretation of the plots is frequently not straightforward due to the effects of internal gradients, wettability and restricted diffusion. T1-T2 measurements can give some indication of fluid saturations as well, but are particularly useful to identify viscosity of the constituents. Beyond these, T1-Diffusion, T2-Internal Gradients, T1-Internal Gradients, T2-T2 exchange, Diffusion-Diffusion exchange, and Diffusion-Diffusion correlation measure are possible measurements, though not commonly performed downhole. While three dimensional (or more) measurements are possible, due to computation power required and the usual low signal to noise of logging measurements, they are not commonly performed.
More simple characterization of diffusion or T1 may be performed using a Dual Te or a Dual Weight Time measurements.
Specialised NMR pulse sequences such as binomial editing may be used to help identify the solid content in a sample versus fluid content. It may also help distinguish kerogen from bitumen.
As indicated, in order to calibrate the NMR logs, a well core has been collected and sent to labs for measurement. Sometimes NMR measurements are made in an as-received state. This may give information regarding the core saturations. However, there are concerns of loss of signal from gas loss during core retrieval, contamination by drilling fluid and core dessication. The sample then needs to be cleaned. This step may range from a few days to a few months depending on the core permeability, type of fluids present and the type of drilling mud used. The sample is then dried and saturated with a synthetic formation brine. NMR measurements are then performed on the core in the 100% brine saturated state. Measurements may be made at ambient conditions, elevated temperature, elevated pressure or both elevated temperature and pressure. The 100% brine saturated state is the standard, but specialized tests may be done where the cores are saturated with oil or possibly a mix of fluids.
The core then needs to be desaturated. For core calibration, this is usually done with air but it may also be performed with lab oil, crude oil, or deuterated oil. Measurements made with lab oil or crude oil will likely require more advanced measurements to interpret the data, for example T2-Diffusion measurements. Depending on the permeability of the system and the desaturation pressure, desaturation may take anywhere from a few days to weeks. NMR measurements are then performed on the core in the desaturated state. Measurements may be made at ambient conditions, elevated temperature, elevated pressure or both elevated temperature and pressure. The T2 cutoff is then calculated by determining the T2 value of the 100% saturated state that has the equivalent as the core in the desaturated state. There are concerns that the NMR results produced in the lab are not representative of downhole conditions.
In addition to the time taken for the NMR measurements, in order to calibrate the NMR permeability, lab permeability measurements must also be made. Usually these are gas permeability measurements performed between sample drying and saturation with brine, but the samples may also be calibrated to liquid permeability measurements if desired. The permeability measurement adds to the time required for the calibration. For shale reservoirs, permeability estimates on cuttings are common using the Gas Research Institute (GRI) technique. However, the accuracy of this technique is uncertain, as there are concerns regarding induced fractures.
Because coring is expensive and time consuming, lab calibration is frequently only performed on a few samples. Typical calibration project sizes range from 2-12 samples. While this is better than no calibration, the complexity of many reservoirs cannot be captured by a low number of samples. The locations of the cored samples may be suboptimal as well, as coring will have taken place before much was known about the individual well.
Some work has been done to perform NMR measurements on drilling cuttings, both at the wellsite and in the lab. There are concerns in understanding what the data from the NMR measurements on cuttings actually mean; the cuttings are assumed to be completely flushed with drilling fluid. There are also concerns of induced fractures in the cuttings from drilling. However, even if the cuttings are intact and filled with a single fluid, the only properties that can be measured with NMR are porosity and T1 and T2 time distributions. Rapid calibration of cutoff times and permeability cannot be performed by using NMR on cuttings.
While NMR provides valuable information about a well, it is one of the slowest logging measurements and one of the more expensive logging tools. It also has the disadvantage of low signal to noise. The low signal to noise can then make analysis of the acquired data more uncertain. Signal to noise can be improved by sacrificing logging speed or performing stationary measurements, but slowing logging speed or stop-and-go movement through an entire formation will be very time consuming.